NavList:

Dear Kermit,

My own investigation of the Unistar Principle is the following.
Sighting one star approximately in the direction of the target,
permits you to adjust the horizontal direction. This is simple.

And this essentially reduce the problem to the problem in one vertical
plane. That is the missile, target, Earth center and star are
in the same vertical plane. What you want to adjust is the
missile velocity direction, using the star altitude.
(The altitude of the missile over the sea level is supposed to be known,
but the distance to the target and the direction of the vertical are
not known exactly).

In this vertical plane, I solve the Kepler problem (of motion of the missile)
for given initial position and velocity. The orbit equation is explicit, and
I write the condition that the orbit (an ellipse) hits the target.

I obtain a condition of the form F(d,v)=0, where d is the distance
to the target
(this is an angle, measured in degrees), and v is the inclination
of the velocity vector (also in degrees). F is in fact
a polynomial of degree 4.

Assuming that we know both d, and v aproximately, we can linearize this
equation (similarly to the Sumner method).

Now what does a star observed altitude give? It gives you d+v, independently
of which star (in this plane) is sighted. If it could give you
another prescribed linear function of the form av+cd, the result of the
linearlization of the equation F(d,v)=0, then this would do the job exactly.
Unfortunately, no star, in this plane or outside, can give you any other
function than d+v.

In other words, "in a given plane passing through the Earth center and the target, if the
sum of the distance to the target and your telescope
inclination to the vertical are given, this already determines how the
starry sky looks".

This implies that more than one star will be redundant, that is the Unistar
Princile is correct, and also implies that you cannot adjust exactly
from any star sites. But you can adjust approximately, and apparently this works.

Alex.

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